Three-dimensional numerical investigation of a single bubble behavior against non-linear forced vibration in a microgravity environment

Abstract

A single gas bubble behavior under non-linear oscillating excitation of the liquid container is studied numerically. The volume of fluid (VOF) method is used for the interface tracking between gas and liquid, implemented in the open source OpenFOAM CFD toolbox. The surface tension force at the interface is evaluated using the continuum surface force (CSF) model. Bubble behavior under forced vibration is examined by considering translational motion and shape deformation of the bubble, while the volume oscillations are ignored regarding the applied frequency range (f < 250 Hz). Bubble response to the forced vibration is studied in three types of regular oscillation, chaotic oscillation, and bubble breakup. It is shown that the inertia of the surrounding liquid and the bubble shape at the beginning of each period have the main effects on the bubble breakup. In order to survey the chaotic response, bubble shape is decomposed into a linear sum of the second to ninth shape modes using Legendre polynomials. The results obtained from the modal analysis of the bubble shape oscillation reveal that the bubble response is regular at frequencies below the second mode natural frequency of the bubble. On the other hand, bubble shape oscillation is chaotic at frequencies close to the third mode natural frequency, which in turn causes the erratic motion of the bubble in the liquid. Finally, the bubble responses to a wide range of frequencies and amplitudes are presented in a diagram based on the Bond number (the ratio of the vibration force to the surface tension force, Bo) and the ratio of the vibration amplitude to the bubble diameter (A/D).